Suppose the Fed raised the FFR to 20%. No bank would bother borrowing from the Fed, and instead borrow from any of the other banks. The EFFR wouldn't really move, since the Fed can't force banks to borrow at that rate. I realize that the Fed is made up of banks, but lets say that one of the larger banks disagrees with the chosen FFR.
From my reading, LIBOR is on its way out, and SOFR is a backwards looking, market rate. Only market participants can move SOFR, correct? If the Fed has no assets on the balance sheet, it can't be a participant.